It'll always catch you out

Martin Vander Weyer reviews A Mathematician Plays the Market by John Allen Paulos

John Allen Paulos is a professor of mathematics in Philadelphia, and used to teach a course called "numbers in the news" at the Columbia School of Journalism. He is also a whimsical humorist in the style of Woody Allen, and can doubtless hold a lecture hall spellbound on the non-predictability of fractal trajectories or the application of the St Petersburg Paradox. He has attempted the same feat here in an analysis of competing methods of stock-picking, based on his own investment follies.

I fear he will leave most readers not much the wiser as to how to enrich themselves, but that may be his intention: having examined all the conventional investment techniques, he dismisses them one by one as at best mathematically unreliable and at worst delusory. His conclusion, in effect, is: don't ever think you're smart enough to beat the market, because the complexity of share price movements, and the scope for deception by all the other players in the game, will always catch you out. Paulos discovered that personally, and is poorer and wiser as a result.

The number in the news that cast a spell over Paulos was the share price of WorldCom. The professor swallowed WorldCom's hype about being "the pre-eminent global communications company for the digital generation" so fervently that he took to emailing its chief executive, the now disgraced Bernie Ebbers, to tell him so.

Having bought the shares at $47, he bought more to "average down" as the price began its inexorable slide. Finally, having missed every opportunity to sell, he watched WorldCom implode into worthlessness after revelations of massive fraud.

You can be wrong about shares for perfectly sound reasons, he concludes, and right for purely accidental ones. You can make as much money picking stocks by throwing darts at the Financial Times as by poring over charts and screens and analysts' reports. You may have good information on which to base share-buying decisions, but you will never know whether you have complete information; and the effect of that information on share prices depends not only on how many other investors have the same information, but on what each of them thinks the others are going to do about it. The outcome, says Paulos, is as predictable as the movement of snooker balls: the tiniest variation in line or speed of the ball first struck creates infinite variations.

But investors remain bizarrely convinced that they know what will happen next. "There is so much complexity in the market, there are so many different measures of success and ways to spin a story, that most people can convince themselves that they've been, or are about to be, inordinately successful," he writes. "If people are desperate enough, they'll manage to find some seeming order in random happenings."

Paulos dismisses as hokum the entire field of "technical analysis", in which devotees base decisions on perceived patterns of share price movement such as "double bottoms". The probability of such patterns repeating themselves on cue is, he points out, mathematically absurd: but probability is a science of which most market players remain wilfully ignorant.

At the other end of the spectrum, Paulos has more respect for the "gimlet-eyed" approach of Warren Buffett, who advises followers to invest as though the stock market did not exist – that is, to identify well-run companies whose products will always be in demand, and invest in them long-term. But Paulos explains why even Buffett's success is deceptive, since the market follows him so slavishly that any share he picks is bound to go up.

Paulos's text mixes high mathematics with the kind of stories that make maths professors laugh – an odd but readable mixture. I liked his outline for a film script about a sports betting scam. And I was struck by his demonstration that if you buy, in alternate weeks, stocks that rise 80 per cent or fall 60 per cent, you may think you will have an average gain of 10 per cent a week and that you will turn $10,000 into $1.4 million in a year – but in fact the likeliest outcome is that you will end up with $1.95.

Many of Paulos's other passages reminded me of Alain de Botton's The Consolations of Philosophy – briefly, you feel you have grasped something very profound, only to find it evaporating moments later. But one lesson certainly remains: don't ever believe anyone who claims to understand how stock markets behave.